Generalization of the Rutherford Formula and Synthesis of Trajectories with Gravity Assist Maneuvers

This article studies the development of new effective methods for designing spacecraft (SC) trajectories for missions using the generalization of the Rutherford formula for the scattering of charged particles proposed by the authors for the case of gravitational scattering. For controlled gravity assist maneuvers of SC, a rule is formulated that makes it possible to purposefully create beams of trajectories with specified properties as a result of a gravity assist maneuver. Modifications of this rule are presented that make it possible to implement efficient and reliable beam recurrent procedures for searching for the ballistic scenarios of interplanetary flights. Of particular importance is the synthesis of sequences of gravity assist maneuvers that provide the given change in the asymptotic velocity of the SC relative to the target planet.